User contributions for Joel2

17:5317:53, 29 June 2024 diff hist +743 N Template:Math/EQ EllipticIntegral01 Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/SpecialFunctions#Complete_Elliptic_Integrals </td> <td align="right"> <math>\frac{2K(k)}{\pi}</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> 1 + \biggl( \frac{1}{2} \biggr)^2k^2 + \biggl( \frac{1\cdot 3}{2\cdot 4}\biggr)^2 k^4 + \biggl( \frac{1\cdot 3\cdot 5}{2^4\cdot 3}\biggr)^2 k^6 + \biggl( \frac{1\cdot 3\cdot..." current
17:5017:50, 29 June 2024 diff hist +1,408 N Template:Math/EQ Gamma01 Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/SpecialFunctions#Gamma_Function </td> <td align="right" colspan="2"> <math>~ \Gamma(z) ~\Gamma(1-z) </math> </td> <td align="center"> <math>~=</math> </td> <td align="left"> <math>~ \frac{\pi}{\sin(\pi z)} </math> </td> <td align="center" rowspan="1"><math>~\biggl|</math></td> <td align="center" rowspan="3"> for example, if <math>~z \..." current
17:4817:48, 29 June 2024 diff hist +25,816 N Appendix/SpecialFunctions Created page with "__FORCETOC__  =50pxSpecial Functions= ===Gamma Function=== <div align="center"> <table border=3 cellpadding=5 cellspacing=1 width="95%" bordercolor="darkblue"> <tr> <th colspan=3 align="center"> Gamma Function </th> </tr> <tr> <td colspan=2> To insert a given equation into any Wiki document, type ... <center> {{ Math/Template_Name</fo..." current
17:4317:43, 29 June 2024 diff hist +1,218 N Template:Math/EQ Toroidal01 Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/Equation_templates#Relationships_Between_Various_Associated_Legendre_Functions </td> <td align="right"> <math> Q_\nu[t t^' - (t^2-1)^{1 / 2} (t^{'2} - 1)^{1 / 2} \cos\psi] </math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> Q_\nu(t) P_\nu(t^') + 2\sum_{n=1}^\infty (-1)^n Q^n_\nu(t) P^{-n}_\nu(t^') \cos(n\psi) </math>..." current
15:1215:12, 29 June 2024 diff hist 0 N File:DysonTorusIllustration03.png No edit summary current
15:0015:00, 29 June 2024 diff hist +203,197 N Apps/DysonPotential Created page with "__FORCETOC__   =Dyson (1893)= {| class="HNM82" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffeeee;" |Dyson (1893) |} Our focus, here, is on the pioneering work of [http://adsabs.harvard.edu/abs/1893RSPTA.184...." current
14:5714:57, 29 June 2024 diff hist 0 N File:FukushimaTorusIllustration02.png No edit summary current
14:5614:56, 29 June 2024 diff hist 0 N File:WongTorusIllustration02.png No edit summary current
14:5514:55, 29 June 2024 diff hist 0 N File:OstrikerTorusIllustration01.png No edit summary current
14:5514:55, 29 June 2024 diff hist 0 N File:MacMillanTorusIllustration02.png No edit summary current
14:5314:53, 29 June 2024 diff hist 0 N File:DysonTorusIllustration04.png No edit summary current
14:4914:49, 29 June 2024 diff hist +14,752 N Appendix/Ramblings/CCGF Created page with "__FORCETOC__   =Compact Cylindrical Green Function (CCGF)= ==Preface by Tohline== [http://adsabs.harvard.edu/abs/1999ApJ...527...86C Cohl & Tohline (1999)] present an expression for the Newtonian gravitational potential in terms of a ''Compact Cylindrical Green's Function'' expansion. Over a professional career that dates back to 1976, this has turned out to be one of my mos..." current
14:4714:47, 29 June 2024 diff hist +5,104 N Apps/DWT Created page with "__FORCETOC__  =Common Theme: Determining the Gravitational Potential for Axisymmetric Mass Distributions= You have arrived at this page from our ''Tiled Menu'' by clicking on the chapter title that is also identified, below, by the light-blue-colored icon. You may proceed directly to that chapter by clicking (again) on that highlighted chapter icon. However, we have brought y..." current

14:1814:18, 28 June 2024 diff hist 0 N File:Figure4THH2012.png No edit summary current
14:1714:17, 28 June 2024 diff hist 0 N File:DiagramToroidalCoordinates.png No edit summary current
14:1614:16, 28 June 2024 diff hist −13 Appendix/Ramblings/ToroidalCoordinates →Summary of Structure
14:1614:16, 28 June 2024 diff hist −13 Appendix/Ramblings/ToroidalCoordinates →Off-center Circle
14:1514:15, 28 June 2024 diff hist 0 N File:LSU CombinedTori.jpg No edit summary current
14:1214:12, 28 June 2024 diff hist +98,482 N Appendix/Ramblings/ToroidalCoordinates Created page with "__FORCETOC__   =Toroidal Configurations and Related Coordinate Systems= This rather long and rambling chapter reveals how my train of thought progressed as I effectively taught myself how to use a toroidal coordinate system to determine the gravitational potential of an axisymmetric configuration. A summary of the key results from this chapter can be found in a primary chapter o..."
14:0714:07, 28 June 2024 diff hist +3 ThreeDimensionalConfigurations/HomogeneousEllipsoids →Oblate Spheroids (a1 = a2 > a3)
13:5313:53, 28 June 2024 diff hist 0 N File:PickettDurisenDavis96Fig1.png No edit summary current
13:4113:41, 28 June 2024 diff hist 0 N File:PP84Tori.jpg No edit summary current
13:3913:39, 28 June 2024 diff hist +28,517 N Apps/PapaloizouPringleTori Created page with "__FORCETOC__  =Massless Polytropic Tori= {| class="HNM82" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffeeee;" |Paploizou-Pringle Tori (1984) |} (''aka'' Papaloizou-Pringle Tori) In a seminal paper that focused on an analysis of nonaxisymmetric instabiliti..."
13:3513:35, 28 June 2024 diff hist +4,309 N Apps/RotatingWhiteDwarfs Created page with "__FORCETOC__  =Rotationally Flattened White Dwarfs= {| class="HNM82" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:white;" |Example Equilibria |} ==Example Equilibrium Co..." current
13:3413:34, 28 June 2024 diff hist +20,391 N Apps/OstrikerBodenheimerLyndenBell66 Created page with "__FORCETOC__  =Rotationally Flattened White Dwarfs= {| class="HNM82" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffeeee;" |Ostriker Bodenheimer & Lynden-Bell (1966) |} As we have reviewed in an SSC/Structure/WhiteDwarfs#Chandrasekhar_mass|acco..." current
13:3213:32, 28 June 2024 diff hist +77,545 N Apps/RotatingPolytropes Created page with "__FORCETOC__  =Rotationally Flattened Polytropes= {| class="HNM82" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:white;" |Example Equilibria |} Here we review what has been learned over the past century+ regarding the structural properties of rotationally flatt..." current
13:2913:29, 28 June 2024 diff hist +15,368 N Apps/ReviewStahler83 Created page with "__FORCETOC__  =Stahler's (1983) Rotationally Flattened Isothermal Configurations= {| class="HNM82" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:white;" |Review of Stahler's (1983) Sol'n Technique |} Consider the collapse of an isothermal cloud (characteriz..." current
13:2313:23, 28 June 2024 diff hist 0 N File:HNM82ThreeDisksAB.png No edit summary current
13:2113:21, 28 June 2024 diff hist +15,126 N Apps/HayashiNaritaMiyama82 Created page with "__FORCETOC__  =Rotationally Flattened Isothermal Structures= {| class="HNM82" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffeeee;" |Hayashi, Narita & Miyama's Analytic Sol'n (1982) |} [https://ui.adsabs.harvard.edu/abs/1982PThPh..68.1949H/abstra..." current
13:1113:11, 28 June 2024 diff hist 0 N File:Q0.5P G1 triangleD.png No edit summary current
13:1013:10, 28 June 2024 diff hist 0 N File:Q0.4P S1 triangleD.png No edit summary current
13:0913:09, 28 June 2024 diff hist 0 N File:Q0.5P G1 squareD.png No edit summary current
13:0813:08, 28 June 2024 diff hist 0 N File:Q0.4P S1 squareD.png No edit summary current
13:0613:06, 28 June 2024 diff hist 0 N File:Q0.5P G1croppedD.png No edit summary current
13:0513:05, 28 June 2024 diff hist 0 N File:Q0.4P S1croppedD.png No edit summary current
13:0313:03, 28 June 2024 diff hist 0 N File:PIA17652-1024x768.png No edit summary current
13:0313:03, 28 June 2024 diff hist 0 N File:Pia18274 full.jpg No edit summary current
13:0113:01, 28 June 2024 diff hist +15,041 N Appendix/Ramblings/Saturn Created page with "__FORCETOC__  =Saturn= Here we draw heavily from the review by [https://ui.adsabs.harvard.edu/abs/2019Sci...364.1046S/abstract L. Spilker (14 June 2019)] titled, ''Cassini-Huygens' exploration of the Saturn system: 13 years of discovery'' that has appeared in Science, Vol. 364, Issue 6445, pp. 1046 - 1051. This review reminds us to emphasize that, although virtually all of the chapters of our H_Book h..." current

17:0317:03, 27 June 2024 diff hist 0 N File:Hachisu86aFig16vConstant.png No edit summary current
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